# Estimation: Sample size

A bank wants to estimate the mean dollars that each card holder will spend each month. It would like to be within plus or minus $10 of the true mean with a 98% confidence level. The standard deviation is thought to be $500. How many card holders should be sampled? After you've determined how many card holders should be sampled, the bank comes back and says that it will cost $5 per sample and they were only planning on spending $10,000 on the sample. In a memo to the bank product development team indicate how many card holders should be sampled to meet the original requirements of the sample. The explain the trade-offs that will occur when you lower the sample to $10,000 to meet their budget.

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#### Solution Preview

Standard deviation =σ= $500

confidence interval= 98%

This is a two tailed test since we are checking for both plus or minus $10

Let the true mean be $μ

What this problem is saying that we should be in the range $μ+10 and $μ-10 and

With sampling we determine the confidence interval of $μ+Z σx and $μ-Z σx

where

Z is read from the normal probability distribution tables corresponding to ...

#### Solution Summary

Estimation-Sample size: The sample size for estimating the mean amount spent by card holders is calculated.